Cylindrical shock wave in a self-gravitating perfect gas with azimuthal magnetic field via Lie group invariance method

2020 ◽  
Vol 17 (10) ◽  
pp. 2050148
Author(s):  
G. Nath ◽  
Arti Devi
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Initial Density ◽  
Density Variation ◽  
Shock Strength ◽  
Adiabatic Exponent ◽  
Perfect Gas ◽  
Azimuthal Magnetic Field ◽  
Cylindrical Shock Wave ◽  
Variation Index

In this paper, we have studied the propagation of cylindrical shock waves in a self-gravitating perfect gas under the influence of azimuthal magnetic field. The method of Lie group invariance is used to construct some special class of self-similar solutions in the presence of the azimuthal magnetic field. The different cases of solutions with a power law and exponential law shock paths are obtained with the choice of arbitrary constants appearing in the expressions for the infinitesimal generators. The similarity solution for cylindrical shock wave with power law shock path is discussed in detail. The effects of variation of Alfven-Mach number, gravitation parameter, initial density variation index and adiabatic exponent on the flow variables are analyzed graphically. It is obtained that the increase in the values of Alfven-Mach number, gravitation parameter and adiabatic exponent have decaying effect on the shock strength. Also, the shock strength increases with an increase in the values of initial density variation index. A comparison is also made between the solutions in gravitating and non-gravitating cases in the presence of magnetic field.

Similarity solutions for magnetogasdynamic cylindrical shock wave in rotating ideal gas using Lie Group theoretic method: Isothermal flow

2020 ◽  
Vol 17 (08) ◽  
pp. 2050123
Author(s):  
G. Nath ◽  
Sumeeta Singh
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Power Law ◽  
Azimuthal Velocity ◽  
Isothermal Flow ◽  
Index Formula ◽  
Shock Strength ◽  
Cylindrical Shock Wave ◽  
Exponential Law ◽  
Variation Index

The propagation of cylindrical shock wave under the influence of axial magnetic field in rotating medium under isothermal flow condition is investigated. The density, magnetic field and azimuthal and axial components of fluid velocity are assumed to be varying in the undisturbed medium. The arbitrary constants appearing in the expressions for infinitesimals of the Local Lie group of transformations bring about three different cases of solutions, i.e. with power law shock path, exponential law shock path and a particular case of power law shock path. Numerical solutions are obtained in the cases of power law and exponential law shock paths. Distribution of gasdynamical quantities are discussed through figures. The effects of variation in values of Alfven-Mach number [Formula: see text], ambient azimuthal velocity index [Formula: see text] and ambient density index [Formula: see text] are studied on flow variables and on shock strength. The numerical integration is done using software Mathematica. It is obtained that magnetic field has a decaying effect on shock strength. Also, increase in value of ambient density or ambient azimuthal velocity variation index in the case of power law shock path and increase in value of ambient density variation index in case of exponential law shock path have the decaying effect on shock strength.

Approximate analytical solution for ionizing cylindrical shock wave in rotational axisymmetric non-ideal gas: isothermal flow

2020 ◽  
Vol 98 (11) ◽  
pp. 1077-1089
Author(s):  
G. Nath ◽  
Sumeeta Singh
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Total Energy ◽  
Fluid Velocity ◽  
Ideal Gas ◽  
Isothermal Flow ◽  
Adiabatic Exponent ◽  
Azimuthal Magnetic Field ◽  
Cylindrical Shock Wave ◽  
Axis Of Symmetry

The propagation of an ionizing cylindrical shock wave in rotational axisymmetric non-ideal gas under isothermal flow condition with an azimuthal magnetic field is investigated. The electrical conductivity is assumed to be negligible in the medium ahead of the shock wave, which after the passage of the shock wave becomes infinitely large. The magnetic pressure, azimuthal fluid velocity, and axial fluid velocity are assumed to be varying according to the power law with distance from the axis of symmetry in the undisturbed medium. The zeroth and first-order approximations are discussed by the aid of the power series method. Solutions for the zeroth-order approximation are constructed in analytical form. Distributions of hydrodynamical quantities are discussed. The effect of flow parameters, namely, shock wave Cowling number c∗, adiabatic exponent γ, rotational parameter L, and gas non-idealness parameter [Formula: see text] are studied on the flow variables. Due to the consideration of a rotating medium or due to the presence of magnetic field, the total energy of the disturbance increases, while with an increase in adiabatic exponent γ the total energy of the disturbance decreases. Density and pressure vanish near the axis of symmetry, thus forming a vacuum there.

scholarly journals A Self-Similar Flow behind a Magnetogasdynamic Shock Wave Generated by a Moving Piston in a Gravitating Gas with Variable Density: Isothermal Flow

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
G. Nath ◽  
A. K. Sinha
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Ambient Medium ◽  
Initial Density ◽  
Power Laws ◽  
Variable Density ◽  
Ideal Gas ◽  
Piston Velocity ◽  
Azimuthal Magnetic Field ◽  
Initial Magnetic Field

The propagation of a cylindrical (or spherical) shock wave in an ideal gas with azimuthal magnetic field and with or without self-gravitational effects is investigated. The shock wave is driven out by a piston moving with time according to power law. The initial density and the initial magnetic field of the ambient medium are assumed to be varying and obeying power laws. Solutions are obtained, when the flow between the shock and the piston is isothermal. The gas is assumed to have infinite electrical conductivity. The shock wave moves with variable velocity, and the total energy of the wave is nonconstant. The effects of variation of the piston velocity exponent (i.e., variation of the initial density exponent), the initial magnetic field exponent, the gravitational parameter, and the Alfven-Mach number on the flow field are obtained. It is investigated that the self-gravitation reduces the effects of the magnetic field. A comparison is also made between gravitating and nongravitating cases.

scholarly journals Magnetogasdynamic Shock Waves in a Rotating Gas with Exponentially Varying Density

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
J. P. Vishwakarma ◽  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Ambient Medium ◽  
Variable Velocity ◽  
Perfect Gas ◽  
Azimuthal Magnetic Field ◽  
One Dimensional ◽  
Adiabatic Flow ◽  
Exponential Law ◽  
Nonsimilar Solutions

Nonsimilar solutions are obtained for one-dimensional adiabatic flow behind a magnetogasdynamic cylindrical shock wave propagating in a rotating or nonrotating perfect gas in presence of a constant azimuthal magnetic field. The density of the gas is assumed to be varying and obeying an exponential law. In order to obtain the solutions, the angular velocity of the ambient medium is assumed to be decreasing exponentially as the distance from the axis increases. The shock wave moves with variable velocity and the total energy of the wave is nonconstant. The effects of variation of Alfven-Mach number and time are obtained. Also, a comparison between the solutions in the cases of rotating and non-rotating media with or without magnetic field is made.

New Self Similar Solution of Spherical Radiative Gasdynamic Shock Wave With Increasing Density Under The Effect Of Axial And Azimuthal Magnetic Field

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Ajay Singh Yadav ◽  
Pravin Kumar Srivastava ◽  
Kishor Kumar Srivastava
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Magnetic Fields ◽  
Initial Density ◽  
Radiation Energy ◽  
Azimuthal Magnetic Field ◽  
Self Similar Solution ◽  
Complete Study ◽  
Self Similar ◽  
Spherical Shock

In the present chapter we investigated the self similar flow behind a spherical shock wave propagating in a medium with increasing density, in the presence of magnetic fields. The medium is assumed to be non gravitational due to the heavy nucleus at origin. The medium ahead and behind the shock front are assumed to be inviscid. The initial density of gas is assumed to vary as some power of distance. It is assumed that gas is grey and opaque. The assumption of optically thick grey gas is physically consistant with the neglect of radiation pressure and radiation energy. Total energy of the flow field behind the spherical shock is assumed to be increasing with time, where the gas ahead of the shock is assumed to be at rest. The results of numerical calculations were shown in the form of graphs. A complete study was made for axial and azimuthal magnetic field. Also the effect of variation of initial density behind the shock, shock velocity and respective magnetic fields were investigated.

Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
G. Nath ◽  
Arti Devi
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Absorption Coefficient ◽  
Power Law ◽  
Similarity Solution ◽  
Adiabatic Exponent ◽  
Rotational Parameter ◽  
Azimuthal Magnetic Field ◽  
Rotating Medium ◽  
Group Invariance

Abstract The propagation of a cylindrical shock wave in rotating medium with azimuthal magnetic field under the action of monochromatic radiation using a method of group invariance is investigated. To derive similarity solutions as well as exact solutions, the group invariance technique is used. All classes of the solutions depending on the absorption coefficient are discussed by considering absorption coefficient to be variable or constant. A similarity solution is obtained, when the absorption coefficient is assumed to be variable. Two cases of solutions with a power law shock path are obtained by the different choices of arbitrary constants involving in the infinitesimal generators of the Lie group of transformations. To obtain the similarity solution in the case of the power law shock path, the density, magnetic field, axial and azimuthal velocity components are assumed to be varying and obeying power laws in the undisturbed medium. It is observed that with increase in the values of Alfven Mach number, adiabatic exponent and rotational parameter, shock strength decreases. The effects of variation of magnetic field strength, adiabatic exponent, rotational parameter and initial magnetic field variation index on the flow variables and on shock waves are analyzed graphically. Also, all classes of exact solutions are obtained by considering a constant absorption coefficient.

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